Fractal growth of tumors and other cellular populations: Linking the mechanistic to the phenomenological modeling and vice versa
By Alberto d'Onofrio. 2009
151 citations recorded by the source corpus.
In this paper we study and extend the mechanistic mean field theory of growth of cellular populations proposed by Mombach et al. [Mombach JCM, Lemke N, Bodmann BEJ, Idiart MAP. A mean-field theory of cellular growth. Europhys Lett 2002;59:923–928] (MLBI model), and we demonstrate that the original model and our generalizations lead to inferences of biological interest. In the first part of this paper, we show that the model in study is widely general since it admits, as particular cases, the main phenomenological models of cellular growth. In the second part of this work, we generalize the MLBI model to a wider family of models by allowing the cells to have a generic unspecified biologically plausible interaction. Then, we derive a relationship between this generic microscopic interaction function and the growth rate of the corresponding macroscopic model. Finally, we propose to use this relationship in order to help the investigation of the biological plausibility of phenomenological models of cancer growth.
Subfields: Modeling and Simulation, Molecular Biology, Physical and Theoretical Chemistry
View Paper: https://www.semanticscholar.org/paper/3c5bc67e8d09972d1e2415cbb1efd676283da4ec
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In Molecular Biology
In Physical and Theoretical Chemistry
Citations in the corpus
- Entropy estimates of small data sets (2008, background): “…a case, one could estimate the probability of each element i to occur, p i , by making some assumption on the probability distribution, as for example (i) parametrizing it [5], (ii) dropping the most unlikely values [6] or (iii) assuming some a priori shape for the probability distribution [7, 8].”
- A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances (2008, unknown): “…without delays has been explored in [2] [4] [5]; the network synchronization problem of complex networks with delays or coupling delays has been studied in [3] [10] [12] [14]; and the literature [9] [11] [13] has been concerned with the adaptive synchronization problem of some dynamical networks.”